AP Physics – Fluids Wrap Up
Here are the equations that you get to play around with:
p = p0 + ! gh
This is the equation for the pressure of something as a function of depth in a fluid.
You would use it to figure out the pressure acting at a depth of 25.0 m in a lake for
example.
FBuoy = !Vg
This is the equation for the buoyant force. It is also an equation that calculates the
weight of an object as a function of its density, volume, and the acceleration of
gravity.
A1v1 = A2v2
This equation represents flow rate, which is the cross sectional area, A, multiplied by
the velocity of the fluid, v. This is set up for two locations in a flow system. The
flow rate for a fluid that is incompressible must stay constant, so this equation allows
you to calculate the linear speed of the fluid as a function of the cross sectional area
of the system.
1
p + ! gy + ! v 2 = const.
2
This is a Bernoulli’s equation. This allows you to calculate pressure, linear speed,
&tc. For a system at different places within the system.
Here is the stuff you need to be able to do.
A. Fluid Mechanics
1. Hydrostatic pressure
a) You should understand that a fluid exerts pressure in all directions.
This is basic. For example, atmospheric pressure goes in all directions about an object –
under it, over it, on the sides, &tc. Good old Pascal’s Principle.
b) You should understand that a fluid at rest exerts pressure perpendicular to any surface
that it contacts.
This is also an application of Pascal’s principle. The pressure is everywhere throughout
the liquid. The direction of the force acting on a surface is always perpendicular to the
surface.
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c) You should understand and be able to use the relationship between pressure and depth
in a liquid, "p = ! g "h .
where p0 would be some initial
pressure. We did a bunch of these problems. Guage pressure is based on the idea that the
atmospheric pressure is zero pressure. Absolute pressure uses a perfect vacuum – zero pascals –
as its zero pressure. So guage pressure differs from absolute pressure by one atmosphere. The
pressure at a certain depth would be give by p = p0 + ! gh . For an absolute pressure you
The actual equation that is provided you is
would set
p0 equal to the atmospheric pressure.
p = p0 + ! gh
For a gage pressure you would drop the
p0
term.
2. Buoyancy
a) You should understand that the difference in the pressure on the upper and lower
surfaces of an object immersed in a liquid results in an upward force on the object.
Because the pressure depends on depth, the pressure increases with the depth. So if the
top of a regular object is 10 m below the surface and the bottom of it is 15 m below – five
meters deeper, the force, which is pressure times area, must be greater. Thus there is a
larger force pushing up on the bottom of the body than the pressure pushing down on the
top of the body. The net force is upward and is given the name of ‘buoyant’ force.
b) You should understand and be able to apply Archimedes’ principle; the buoyant force on
a submersed object is equal to the weight of the liquid it displaces.
Well, the statement gives you Archimedes’ principle and tells you to understand it. So do
that.
3. Fluid flow continuity
a) You should understand that for laminar flow, the flow rate of a liquid through its cross
section is the same at any point along its path.
So okay, do that too.
b) You understand and be able to apply the equation of continuity, !1 A1v1 = ! 2 A2v2 .
Actually the equation that you are given is: A1v1 = A2v2 the density part isn’t in the
equation. This is because in the type of problem that you’ll be doing, the density won’t change and
will remain constant. Because of that, it cancels out of the equation. The Physics Kahuna is not
at all sure why statement b) above had a different form of the equation. Probably some
miscommunication at the College Board. Anyway, we did a bunch of problems where you got
to use the equation. It is all pie.
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4. Bernoulli’s equation
a) You should understand that the pressure of a flowing liquid is low where the velocity is
high, and vice versa.
Simple principle, simple stuff. Hey you can do it!
b) You should understand and be able to apply Bernoulli’s equation,
1
p + ! gy + ! v 2 = const.
2
Table of Density Values for Various Substances
Substance
kg/m3
Air
1.20
Carbon dioxide 1.84
Helium
0.17
Hydrogen
0.084
Methane
0.67
Nitrogen
1.16
Oxygen
1.33
Steam (100°C) 1.99
Gases
Alcohol, ethyl
Aluminum
Copper
Gold
Granite
Ice
Brass
Iron
Silver
Lead
Mercury
Marble
Oil
Quartz
Rubber
Seawater
Styrofoam
Water
Wood
Density
kg/m3
0.791 x 103
2.70 x 103
8.9 x 103
19.3 x 103
2.7 x 103
0.917 x 103
4.70 x 103
7.8 x 103
10.5 x 103
11.3 x 103
13.6 x 103
2.7 x 103
0.85 x 103
2.65 x 103
1.15 x 103
1.025 x 103
0.10 x 103
1.000 x 103
0.50 x 103
In metric units, a column of air with an area of one square meter weighs 1.013 x 10 5 N (at sea
level). Therefore, atmospheric pressure would be 1.013 x 105 Pa or 1.013 x 102 kPa (or 101.3 kPa).
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